// $Id: Array.hh 249 2008-11-20 09:58:23Z schaerf $
// This file is part of EasyLocalpp: a C++ Object-Oriented framework
// aimed at easing the development of Local Search algorithms.
// Copyright (C) 2001--2008 Andrea Schaerf, Luca Di Gaspero. 
//
// This software may be modified and distributed under the terms
// of the MIT license.  See the LICENSE file for details.

#if !defined(_ARRAY_HH)
#define _ARRAY_HH

#include <set>
#include <stdexcept>
#include <iostream>
#include <iomanip>
#include <cmath>
#include <cstdlib>

namespace QPArray
{

	enum MType { DIAG };

	template <typename T>
	class Vector
	{
	public: 
		Vector(); 
		Vector(const unsigned int n);  
		Vector(const T& a, const unsigned int n); //initialize to constant value 
		Vector(const T* a, const unsigned int n); // Initialize to array 
		Vector(const Vector &rhs); // copy constructor 
		~Vector(); // destructor

		inline void set(const T* a, const unsigned int n);
		Vector<T> extract(const std::set<unsigned int>& indexes) const;
		inline T& operator[](const unsigned int& i); //i-th element 
		inline const T& operator[](const unsigned int& i) const; 

		inline unsigned int size() const;
		inline void resize(const unsigned int n);
		inline void resize(const T& a, const unsigned int n);

		Vector<T>& operator=(const Vector<T>& rhs); //assignment 
		Vector<T>& operator=(const T& a); //assign a to every element 
		inline Vector<T>& operator+=(const Vector<T>& rhs);
		inline Vector<T>& operator-=(const Vector<T>& rhs);
		inline Vector<T>& operator*=(const Vector<T>& rhs);
		inline Vector<T>& operator/=(const Vector<T>& rhs);
		inline Vector<T>& operator^=(const Vector<T>& rhs);
		inline Vector<T>& operator+=(const T& a);
		inline Vector<T>& operator-=(const T& a);
		inline Vector<T>& operator*=(const T& a);
		inline Vector<T>& operator/=(const T& a);
		inline Vector<T>& operator^=(const T& a);
	private: 
		unsigned int n; // size of array. upper index is n-1 
		T* v; // storage for data
	}; 

	template <typename T> 
	Vector<T>::Vector() 
		: n(0), v(0) 
	{} 

	template <typename T> 
	Vector<T>::Vector(const unsigned int n) 
		: v(new T[n]) 
	{
		this->n = n;
	} 

	template <typename T> 
	Vector<T>::Vector(const T& a, const unsigned int n) 
		: v(new T[n])
	{ 
		this->n = n;
		for (unsigned int i = 0; i < n; i++) 
			v[i] = a; 
	} 

	template <typename T> 
	Vector<T>::Vector(const T* a, const unsigned int n) 
		: v(new T[n])
	{ 
		this->n = n;
		for (unsigned int i = 0; i < n; i++) 
			v[i] = *a++; 
	} 

	template <typename T> 
	Vector<T>::Vector(const Vector<T>& rhs) 
		: v(new T[rhs.n])
	{ 
		this->n = rhs.n;
		for (unsigned int	i = 0; i < n; i++) 
			v[i] = rhs[i]; 
	} 

	template <typename T> 
	Vector<T>::~Vector() 
	{ 
		if (v != 0) 
			delete[] (v); 
	} 

	template <typename T> 
	void Vector<T>::resize(const unsigned int n) 
	{
		if (n == this->n)
			return;
		if (v != 0) 
			delete[] (v); 
		v = new T[n];
		this->n = n;
	} 

	template <typename T> 
	void Vector<T>::resize(const T& a, const unsigned int n) 
	{
		resize(n);
		for (unsigned int i = 0; i < n; i++)
			v[i] = a;
	} 


	template <typename T> 
	inline Vector<T>& Vector<T>::operator=(const Vector<T>& rhs) 
		// postcondition: normal assignment via copying has been performed; 
		// if vector and rhs were different sizes, vector 
		// has been resized to match the size of rhs 
	{ 
		if (this != &rhs) 
		{ 
			resize(rhs.n);
			for (unsigned int i = 0; i < n; i++) 
				v[i] = rhs[i]; 
		} 
		return *this; 
	} 

	template <typename T> 
	inline Vector<T> & Vector<T>::operator=(const T& a) //assign a to every element 
	{ 
		for (unsigned int i = 0; i < n; i++) 
			v[i] = a; 
		return *this; 
	} 

	template <typename T> 
	inline T & Vector<T>::operator[](const unsigned int& i) //subscripting 
	{ 
		return v[i]; 
	}

	template <typename T>
	inline const T& Vector<T>::operator[](const unsigned int& i) const //subscripting 
	{ 
		return v[i]; 
	} 

	template <typename T> 
	inline unsigned int Vector<T>::size() const 
	{ 
		return n; 
	}

	template <typename T> 
	inline void Vector<T>::set(const T* a, unsigned int n) 
	{ 
		resize(n);
		for (unsigned int i = 0; i < n; i++) 
			v[i] = a[i]; 
	} 

	template <typename T> 
	inline Vector<T> Vector<T>::extract(const std::set<unsigned int>& indexes) const
	{
		Vector<T> tmp(indexes.size());
		unsigned int i = 0;

		for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
		{
			if (*el >= n)
				throw std::logic_error("Error extracting subvector: the indexes are out of vector bounds");
			tmp[i++] = v[*el];
		}

		return tmp;
	}

	template <typename T> 
	inline Vector<T>& Vector<T>::operator+=(const Vector<T>& rhs)
	{
		if (this->size() != rhs.size())
			throw std::logic_error("Operator+=: vectors have different sizes");
		for (unsigned int i = 0; i < n; i++)
			v[i] += rhs[i];

		return *this;
	}


	template <typename T> 
	inline Vector<T>& Vector<T>::operator+=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			v[i] += a;

		return *this;
	}

	template <typename T>
	inline Vector<T> operator+(const Vector<T>& rhs)
	{
		return rhs;
	}

	template <typename T>
	inline Vector<T> operator+(const Vector<T>& lhs, const Vector<T>& rhs)
	{
		if (lhs.size() != rhs.size())
			throw std::logic_error("Operator+: vectors have different sizes");
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] + rhs[i];

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator+(const Vector<T>& lhs, const T& a)
	{
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] + a;

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator+(const T& a, const Vector<T>& rhs)
	{
		Vector<T> tmp(rhs.size());
		for (unsigned int i = 0; i < rhs.size(); i++)
			tmp[i] = a + rhs[i];

		return tmp;
	}

	template <typename T> 
	inline Vector<T>& Vector<T>::operator-=(const Vector<T>& rhs)
	{
		if (this->size() != rhs.size())
			throw std::logic_error("Operator-=: vectors have different sizes");
		for (unsigned int i = 0; i < n; i++)
			v[i] -= rhs[i];

		return *this;
	}


	template <typename T> 
	inline Vector<T>& Vector<T>::operator-=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			v[i] -= a;

		return *this;
	}

	template <typename T>
	inline Vector<T> operator-(const Vector<T>& rhs)
	{
		return (T)(-1) * rhs;
	}

	template <typename T>
	inline Vector<T> operator-(const Vector<T>& lhs, const Vector<T>& rhs)
	{
		if (lhs.size() != rhs.size())
			throw std::logic_error("Operator-: vectors have different sizes");
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] - rhs[i];

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator-(const Vector<T>& lhs, const T& a)
	{
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] - a;

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator-(const T& a, const Vector<T>& rhs)
	{
		Vector<T> tmp(rhs.size());
		for (unsigned int i = 0; i < rhs.size(); i++)
			tmp[i] = a - rhs[i];

		return tmp;
	}

	template <typename T> 
	inline Vector<T>& Vector<T>::operator*=(const Vector<T>& rhs)
	{
		if (this->size() != rhs.size())
			throw std::logic_error("Operator*=: vectors have different sizes");
		for (unsigned int i = 0; i < n; i++)
			v[i] *= rhs[i];

		return *this;
	}


	template <typename T> 
	inline Vector<T>& Vector<T>::operator*=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			v[i] *= a;

		return *this;
	}

	template <typename T>
	inline Vector<T> operator*(const Vector<T>& lhs, const Vector<T>& rhs)
	{
		if (lhs.size() != rhs.size())
			throw std::logic_error("Operator*: vectors have different sizes");
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] * rhs[i];

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator*(const Vector<T>& lhs, const T& a)
	{
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] * a;

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator*(const T& a, const Vector<T>& rhs)
	{
		Vector<T> tmp(rhs.size());
		for (unsigned int i = 0; i < rhs.size(); i++)
			tmp[i] = a * rhs[i];

		return tmp;
	}

	template <typename T> 
	inline Vector<T>& Vector<T>::operator/=(const Vector<T>& rhs)
	{
		if (this->size() != rhs.size())
			throw std::logic_error("Operator/=: vectors have different sizes");
		for (unsigned int i = 0; i < n; i++)
			v[i] /= rhs[i];

		return *this;
	}


	template <typename T> 
	inline Vector<T>& Vector<T>::operator/=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			v[i] /= a;

		return *this;
	}

	template <typename T>
	inline Vector<T> operator/(const Vector<T>& lhs, const Vector<T>& rhs)
	{
		if (lhs.size() != rhs.size())
			throw std::logic_error("Operator/: vectors have different sizes");
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] / rhs[i];

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator/(const Vector<T>& lhs, const T& a)
	{
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = lhs[i] / a;

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator/(const T& a, const Vector<T>& rhs)
	{
		Vector<T> tmp(rhs.size());
		for (unsigned int i = 0; i < rhs.size(); i++)
			tmp[i] = a / rhs[i];

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator^(const Vector<T>& lhs, const Vector<T>& rhs)
	{
		if (lhs.size() != rhs.size())
			throw std::logic_error("Operator^: vectors have different sizes");
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = pow(lhs[i], rhs[i]);

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator^(const Vector<T>& lhs, const T& a)
	{
		Vector<T> tmp(lhs.size());
		for (unsigned int i = 0; i < lhs.size(); i++)
			tmp[i] = pow(lhs[i], a);

		return tmp;
	}

	template <typename T>
	inline Vector<T> operator^(const T& a, const Vector<T>& rhs)
	{
		Vector<T> tmp(rhs.size());
		for (unsigned int i = 0; i < rhs.size(); i++)
			tmp[i] = pow(a, rhs[i]);

		return tmp;
	}

	template <typename T>
	inline Vector<T>& Vector<T>::operator^=(const Vector<T>& rhs)
	{
		if (this->size() != rhs.size())
			throw std::logic_error("Operator^=: vectors have different sizes");
		for (unsigned int i = 0; i < n; i++)
			v[i] = pow(v[i], rhs[i]);

		return *this;
	}

	template <typename T>
	inline Vector<T>& Vector<T>::operator^=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			v[i] = pow(v[i], a);

		return *this;
	}

	template <typename T>
	inline bool operator==(const Vector<T>& v, const Vector<T>& w)
	{
		if (v.size() != w.size())
			throw std::logic_error("Vectors of different size are not confrontable");
		for (unsigned i = 0; i < v.size(); i++)
			if (v[i] != w[i])
				return false;
		return true;
	}

	template <typename T>
	inline bool operator!=(const Vector<T>& v, const Vector<T>& w)
	{
		if (v.size() != w.size())
			throw std::logic_error("Vectors of different size are not confrontable");
		for (unsigned i = 0; i < v.size(); i++)
			if (v[i] != w[i])
				return true;
		return false;
	}

	template <typename T>
	inline bool operator<(const Vector<T>& v, const Vector<T>& w)
	{
		if (v.size() != w.size())
			throw std::logic_error("Vectors of different size are not confrontable");
		for (unsigned i = 0; i < v.size(); i++)
			if (v[i] >= w[i])
				return false;
		return true;
	}

	template <typename T>
	inline bool operator<=(const Vector<T>& v, const Vector<T>& w)
	{
		if (v.size() != w.size())
			throw std::logic_error("Vectors of different size are not confrontable");
		for (unsigned i = 0; i < v.size(); i++)
			if (v[i] > w[i])
				return false;
		return true;
	}

	template <typename T>
	inline bool operator>(const Vector<T>& v, const Vector<T>& w)
	{
		if (v.size() != w.size())
			throw std::logic_error("Vectors of different size are not confrontable");
		for (unsigned i = 0; i < v.size(); i++)
			if (v[i] <= w[i])
				return false;
		return true;
	}

	template <typename T>
	inline bool operator>=(const Vector<T>& v, const Vector<T>& w)
	{
		if (v.size() != w.size())
			throw std::logic_error("Vectors of different size are not confrontable");
		for (unsigned i = 0; i < v.size(); i++)
			if (v[i] < w[i])
				return false;
		return true;
	}

	/**
	Input/Output 
	*/
	template <typename T>
	inline std::ostream& operator<<(std::ostream& os, const Vector<T>& v)
	{
		os << std::endl << v.size() << std::endl;
		for (unsigned int i = 0; i < v.size() - 1; i++)
			os << std::setw(20) << std::setprecision(16) << v[i] << ", ";
		os << std::setw(20) << std::setprecision(16) << v[v.size() - 1] << std::endl;

		return os;
	}

	template <typename T>
	std::istream& operator>>(std::istream& is, Vector<T>& v)
	{
		int elements;
		char comma;
		is >> elements;
		v.resize(elements);
		for (unsigned int i = 0; i < elements; i++)
			is >> v[i] >> comma;

		return is;
	}

	/**
	Index utilities
	*/

	std::set<unsigned int> seq(unsigned int s, unsigned int e);

	std::set<unsigned int> singleton(unsigned int i);

	template <typename T>
	class CanonicalBaseVector : public Vector<T>
	{
	public:
		CanonicalBaseVector(unsigned int i, unsigned int n);
		inline void reset(unsigned int i);
	private:
		unsigned int e;
	};

	template <typename T>
	CanonicalBaseVector<T>::CanonicalBaseVector(unsigned int i, unsigned int n)
		: Vector<T>((T)0, n), e(i)
	{ (*this)[e] = (T)1; }

	template <typename T>
	inline void CanonicalBaseVector<T>::reset(unsigned int i)
	{ 
		(*this)[e] = (T)0; 
		e = i; 
		(*this)[e] = (T)1;
	}

#include <stdexcept>

	template <typename T>
	inline T sum(const Vector<T>& v)
	{
		T tmp = (T)0;
		for (unsigned int i = 0; i < v.size(); i++)
			tmp += v[i];

		return tmp;
	}

	template <typename T>
	inline T prod(const Vector<T>& v)
	{
		T tmp = (T)1;
		for (unsigned int i = 0; i < v.size(); i++)
			tmp *= v[i];

		return tmp;
	}

	template <typename T>
	inline T mean(const Vector<T>& v)
	{
		T sum = (T)0;
		for (unsigned int i = 0; i < v.size(); i++)
			sum += v[i];
		return sum / v.size();
	}

	template <typename T>
	inline T median(const Vector<T>& v)
	{
		Vector<T> tmp = sort(v);
		if (v.size() % 2 == 1) // it is an odd-sized vector
			return tmp[v.size() / 2];
		else
			return 0.5 * (tmp[v.size() / 2 - 1] + tmp[v.size() / 2]);
	}

	template <typename T>
	inline T stdev(const Vector<T>& v, bool sample_correction = false)
	{
		return sqrt(var(v, sample_correction));
	}

	template <typename T>
	inline T var(const Vector<T>& v, bool sample_correction = false)
	{
		T sum = (T)0, ssum = (T)0;
		unsigned int n = v.size();
		for (unsigned int i = 0; i < n; i++)
		{	
			sum += v[i];
			ssum += (v[i] * v[i]);
		}
		if (!sample_correction)
			return (ssum / n) - (sum / n) * (sum / n);
		else
			return n * ((ssum / n) - (sum / n) * (sum / n)) / (n - 1);
	}

/*	template <typename T>
	inline T max(const Vector<T>& v)
	{
		T value = v[0];
		for (unsigned int i = 1; i < v.size(); i++)
			value = std::max(v[i], value);

		return value;
	}

	template <typename T>
	inline T min(const Vector<T>& v)
	{
		T value = v[0];
		for (unsigned int i = 1; i < v.size(); i++)
			value = std::min(v[i], value);

		return value;
	}

	template <typename T>
	inline unsigned int index_max(const Vector<T>& v)
	{
		unsigned int max = 0;
		for (unsigned int i = 1; i < v.size(); i++)
			if (v[i] > v[max])
				max = i;

		return max;
	}

	template <typename T>
	inline unsigned int index_min(const Vector<T>& v)
	{
		unsigned int min = 0;
		for (unsigned int i = 1; i < v.size(); i++)
			if (v[i] < v[min])
				min = i;

		return min;
	}*/


	template <typename T>
	inline T dot_prod(const Vector<T>& a, const Vector<T>& b)
	{
		T sum = (T)0;
		if (a.size() != b.size())
			throw std::logic_error("Dotprod error: the vectors are not the same size");
		for (unsigned int i = 0; i < a.size(); i++)
			sum += a[i] * b[i];

		return sum;
	}

	/**
	Single element mathematical functions
	*/

	template <typename T>
	inline Vector<T> exp(const Vector<T>& v)
	{
		Vector<T> tmp(v.size());
		for (unsigned int i = 0; i < v.size(); i++)
			tmp[i] = exp(v[i]);

		return tmp;
	}

	template <typename T>
	inline Vector<T> log(const Vector<T>& v)
	{
		Vector<T> tmp(v.size());
		for (unsigned int i = 0; i < v.size(); i++)
			tmp[i] = log(v[i]);

		return tmp;
	}

	template <typename T>
	inline Vector<T> sqrt(const Vector<T>& v)
	{
		Vector<T> tmp(v.size());
		for (unsigned int i = 0; i < v.size(); i++)
			tmp[i] = sqrt(v[i]);

		return tmp;
	}

	template <typename T>
	inline Vector<T> pow(const Vector<T>& v, double a)
	{
		Vector<T> tmp(v.size());
		for (unsigned int i = 0; i < v.size(); i++)
			tmp[i] = pow(v[i], a);

		return tmp;
	}

	template <typename T>
	inline Vector<T> abs(const Vector<T>& v)
	{
		Vector<T> tmp(v.size());
		for (unsigned int i = 0; i < v.size(); i++)
			tmp[i] = (T)fabs(v[i]);

		return tmp;
	}

	template <typename T>
	inline Vector<T> sign(const Vector<T>& v)
	{
		Vector<T> tmp(v.size());
		for (unsigned int i = 0; i < v.size(); i++)
			tmp[i] = v[i] > 0 ? +1 : v[i] == 0 ? 0 : -1;

		return tmp;
	}

	template <typename T>
	inline unsigned int partition(Vector<T>& v, unsigned int begin, unsigned int end)
	{
		unsigned int i = begin + 1, j = begin + 1;
		T pivot = v[begin];
		while (j <= end) 
		{
			if (v[j] < pivot) {
				std::swap(v[i], v[j]);
				i++;
			}
			j++;
		}
		v[begin] = v[i - 1];
		v[i - 1] = pivot;
		return i - 2;
	}


	template <typename T>
	inline void quicksort(Vector<T>& v, unsigned int begin, unsigned int end)
	{
		if (end > begin)
		{
			unsigned int index = partition(v, begin, end);
			quicksort(v, begin, index);
			quicksort(v, index + 2, end);
		}
	}

	template <typename T>
	inline Vector<T> sort(const Vector<T>& v)
	{
		Vector<T> tmp(v);

		quicksort<T>(tmp, 0, tmp.size() - 1);

		return tmp;
	}

	template <typename T>
	inline Vector<double> rank(const Vector<T>& v)
	{
		Vector<T> tmp(v);
		Vector<double> tmp_rank(0.0, v.size());	

		for (unsigned int i = 0; i < tmp.size(); i++)
		{
			unsigned int smaller = 0, equal = 0;
			for (unsigned int j = 0; j < tmp.size(); j++)
				if (i == j)
					continue;
				else
					if (tmp[j] < tmp[i])
						smaller++;
					else if (tmp[j] == tmp[i])
						equal++;
			tmp_rank[i] = smaller + 1;
			if (equal > 0)
			{
				for (unsigned int j = 1; j <= equal; j++)
					tmp_rank[i] += smaller + 1 + j;
				tmp_rank[i] /= (double)(equal + 1);
			}
		}

		return tmp_rank;
	}

	//enum MType { DIAG };

	template <typename T>
	class Matrix 
	{
	public:
		Matrix(); // Default constructor
		Matrix(const unsigned int n, const unsigned int m); // Construct a n x m matrix
		Matrix(const T& a, const unsigned int n, const unsigned int m); // Initialize the content to constant a
		Matrix(MType t, const T& a, const T& o, const unsigned int n, const unsigned int m);
		Matrix(MType t, const Vector<T>& v, const T& o, const unsigned int n, const unsigned int m);
		Matrix(const T* a, const unsigned int n, const unsigned int m); // Initialize to array 
		Matrix(const Matrix<T>& rhs); // Copy constructor
		~Matrix(); // destructor

		inline T* operator[](const unsigned int& i) { return v[i]; } // Subscripting: row i
		inline const T* operator[](const unsigned int& i) const { return v[i]; }; // const subsctipting

		inline void resize(const unsigned int n, const unsigned int m);
		inline void resize(const T& a, const unsigned int n, const unsigned int m);


		inline Vector<T> extractRow(const unsigned int i) const; 
		inline Vector<T> extractColumn(const unsigned int j) const;
		inline Vector<T> extractDiag() const;
		inline Matrix<T> extractRows(const std::set<unsigned int>& indexes) const;
		inline Matrix<T> extractColumns(const std::set<unsigned int>& indexes) const;
		inline Matrix<T> extract(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes) const;

		inline void set(const T* a, unsigned int n, unsigned int m);
		inline void set(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes, const Matrix<T>& m);
		inline void setRow(const unsigned int index, const Vector<T>& v);
		inline void setRow(const unsigned int index, const Matrix<T>& v);
		inline void setRows(const std::set<unsigned int>& indexes, const Matrix<T>& m);
		inline void setColumn(const unsigned int index, const Vector<T>& v);
		inline void setColumn(const unsigned int index, const Matrix<T>& v);
		inline void setColumns(const std::set<unsigned int>& indexes, const Matrix<T>& m);


		inline unsigned int nrows() const { return n; } // number of rows
		inline unsigned int ncols() const { return m; } // number of columns

		inline Matrix<T>& operator=(const Matrix<T>& rhs); // Assignment operator
		inline Matrix<T>& operator=(const T& a); // Assign to every element value a
		inline Matrix<T>& operator+=(const Matrix<T>& rhs);
		inline Matrix<T>& operator-=(const Matrix<T>& rhs);
		inline Matrix<T>& operator*=(const Matrix<T>& rhs);
		inline Matrix<T>& operator/=(const Matrix<T>& rhs);
		inline Matrix<T>& operator^=(const Matrix<T>& rhs);
		inline Matrix<T>& operator+=(const T& a);
		inline Matrix<T>& operator-=(const T& a);
		inline Matrix<T>& operator*=(const T& a);
		inline Matrix<T>& operator/=(const T& a);
		inline Matrix<T>& operator^=(const T& a);
		inline operator Vector<T>();
	private:
		unsigned int n; // number of rows
		unsigned int m; // number of columns
		T **v; // storage for data
	};

	template <typename T>
	Matrix<T>::Matrix() 
		: n(0), m(0), v(0)
	{}

	template <typename T>
	Matrix<T>::Matrix(unsigned int n, unsigned int m)
		: v(new T*[n])
	{
		register unsigned int i;
		this->n = n; this->m = m;
		v[0] = new T[m * n];
		for (i = 1; i < n; i++)
			v[i] = v[i - 1] + m;
	}

	template <typename T>
	Matrix<T>::Matrix(const T& a, unsigned int n, unsigned int m)
		: v(new T*[n])
	{
		register unsigned int i, j;
		this->n = n; this->m = m;
		v[0] = new T[m * n];
		for (i = 1; i < n; i++)
			v[i] = v[i - 1] + m;
		for (i = 0; i < n; i++)
			for (j = 0; j < m; j++)
				v[i][j] = a;
	}

	template <class T> 
	Matrix<T>::Matrix(const T* a, unsigned int n, unsigned int m) 
		: v(new T*[n])
	{ 
		register unsigned int i, j;
		this->n = n; this->m = m;
		v[0] = new T[m * n]; 
		for (i = 1; i < n; i++) 
			v[i] = v[i - 1] + m; 
		for (i = 0; i < n; i++) 
			for (j = 0; j < m; j++) 
				v[i][j] = *a++; 
	} 

	template <class T> 
	Matrix<T>::Matrix(MType t, const T& a, const T& o, unsigned int n, unsigned int m) 
		: v(new T*[n])
	{ 
		register unsigned int i, j;
		this->n = n; this->m = m;
		v[0] = new T[m * n]; 
		for (i = 1; i < n; i++) 
			v[i] = v[i - 1] + m; 
		switch (t)
		{
		case DIAG:
			for (i = 0; i < n; i++) 
				for (j = 0; j < m; j++) 
					if (i != j)
						v[i][j] = o; 
					else
						v[i][j] = a;
			break;
		default:
			throw std::logic_error("Matrix type not supported");
		}
	} 

	template <class T> 
	Matrix<T>::Matrix(MType t, const Vector<T>& a, const T& o, unsigned int n, unsigned int m) 
		: v(new T*[n])
	{ 
		register unsigned int i, j;
		this->n = n; this->m = m;
		v[0] = new T[m * n]; 
		for (i = 1; i < n; i++) 
			v[i] = v[i - 1] + m; 
		switch (t)
		{
		case DIAG:
			for (i = 0; i < n; i++) 
				for (j = 0; j < m; j++) 
					if (i != j)
						v[i][j] = o; 
					else
						v[i][j] = a[i];
			break;
		default:
			throw std::logic_error("Matrix type not supported");
		}
	} 

	template <typename T>
	Matrix<T>::Matrix(const Matrix<T>& rhs)
		: v(new T*[rhs.n])
	{
		register unsigned int i, j;
		n = rhs.n; m = rhs.m;
		v[0] = new T[m * n]; 
		for (i = 1; i < n; i++) 
			v[i] = v[i - 1] + m;
		for (i = 0; i < n; i++)
			for (j = 0; j < m; j++)
				v[i][j] = rhs[i][j];
	}

	template <typename T> 
	Matrix<T>::~Matrix() 
	{ 
		if (v != 0) { 
			delete[] (v[0]); 
			delete[] (v); 
		} 
	}

	template <typename T> 
	inline Matrix<T>& Matrix<T>::operator=(const Matrix<T> &rhs) 
		// postcondition: normal assignment via copying has been performed; 
		// if matrix and rhs were different sizes, matrix 
		// has been resized to match the size of rhs 
	{ 
		register unsigned int i, j;
		if (this != &rhs) 
		{
			resize(rhs.n, rhs.m);
			for (i = 0; i < n; i++) 
				for (j = 0; j < m; j++) 
					v[i][j] = rhs[i][j]; 
		} 
		return *this; 
	} 

	template <typename T> 
	inline Matrix<T>& Matrix<T>::operator=(const T& a) // assign a to every element 
	{ 
		register unsigned int i, j;
		for (i = 0; i < n; i++) 
			for (j = 0; j < m; j++) 
				v[i][j] = a; 
		return *this; 
	} 


	template <typename T> 
	inline void Matrix<T>::resize(const unsigned int n, const unsigned int m) 
	{
		register unsigned int i;
		if (n == this->n && m == this->m)
			return;
		if (v != 0) 
		{ 
			delete[] (v[0]); 
			delete[] (v); 
		} 
		this->n = n; this->m = m;
		v = new T*[n]; 
		v[0] = new T[m * n];  
		for (i = 1; i < n; i++)
			v[i] = v[i - 1] + m;
	} 

	template <typename T> 
	inline void Matrix<T>::resize(const T& a, const unsigned int n, const unsigned int m) 
	{
		register unsigned int i, j;
		resize(n, m);
		for (i = 0; i < n; i++)
			for (j = 0; j < m; j++)
				v[i][j] = a;
	} 



	template <typename T> 
	inline Vector<T> Matrix<T>::extractRow(const unsigned int i) const
	{
		if (i >= n)
			throw std::logic_error("Error in extractRow: trying to extract a row out of matrix bounds");
		Vector<T> tmp(v[i], m);

		return tmp;
	}

	template <typename T> 
	inline Vector<T> Matrix<T>::extractColumn(const unsigned int j) const
	{
		register unsigned int i;
		if (j >= m)
			throw std::logic_error("Error in extractRow: trying to extract a row out of matrix bounds");
		Vector<T> tmp(n);

		for (i = 0; i < n; i++)
			tmp[i] = v[i][j];

		return tmp;
	}

	template <typename T>
	inline Vector<T> Matrix<T>::extractDiag() const
	{
		register unsigned int d = std::min(n, m), i;

		Vector<T> tmp(d);

		for (i = 0; i < d; i++)
			tmp[i] = v[i][i];

		return tmp;

	}

	template <typename T> 
	inline Matrix<T> Matrix<T>::extractRows(const std::set<unsigned int>& indexes) const
	{
		Matrix<T> tmp(indexes.size(), m);
		register unsigned int i = 0, j;

		for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
		{
			for (j = 0; j < m; j++)
			{
				if (*el >= n)
					throw std::logic_error("Error extracting rows: the indexes are out of matrix bounds");
				tmp[i][j] = v[*el][j];
			}
			i++;
		}

		return tmp;
	}

	template <typename T> 
	inline Matrix<T> Matrix<T>::extractColumns(const std::set<unsigned int>& indexes) const
	{
		Matrix<T> tmp(n, indexes.size());
		register unsigned int i, j = 0;

		for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
		{
			for (i = 0; i < n; i++)
			{
				if (*el >= m)
					throw std::logic_error("Error extracting columns: the indexes are out of matrix bounds");
				tmp[i][j] = v[i][*el];
			}
			j++;
		}

		return tmp;
	}

	template <typename T> 
	inline Matrix<T> Matrix<T>::extract(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes) const
	{
		Matrix<T> tmp(r_indexes.size(), c_indexes.size());
		register unsigned int i = 0, j;

		for (std::set<unsigned int>::const_iterator r_el = r_indexes.begin(); r_el != r_indexes.end(); r_el++)
		{
			if (*r_el >= n)
				throw std::logic_error("Error extracting submatrix: the indexes are out of matrix bounds");
			j = 0;
			for (std::set<unsigned int>::const_iterator c_el = c_indexes.begin(); c_el != c_indexes.end(); c_el++)
			{
				if (*c_el >= m)
					throw std::logic_error("Error extracting rows: the indexes are out of matrix bounds");
				tmp[i][j] = v[*r_el][*c_el];
				j++;
			}
			i++;
		}

		return tmp;
	}

	template <typename T> 
	inline void Matrix<T>::setRow(unsigned int i, const Vector<T>& a)
	{	
		if (i >= n)
			throw std::logic_error("Error in setRow: trying to set a row out of matrix bounds");
		if (this->m != a.size())
			throw std::logic_error("Error setting matrix row: ranges are not compatible");
		for (unsigned int j = 0; j < ncols(); j++)
			v[i][j] = a[j];
	}

	template <typename T> 
	inline void Matrix<T>::setRow(unsigned int i, const Matrix<T>& a)
	{	
		if (i >= n)
			throw std::logic_error("Error in setRow: trying to set a row out of matrix bounds");
		if (this->m != a.ncols())
			throw std::logic_error("Error setting matrix column: ranges are not compatible");
		if (a.nrows() != 1)
			throw std::logic_error("Error setting matrix column with a non-row matrix");
		for (unsigned int j = 0; j < ncols(); j++)
			v[i][j] = a[0][j];
	}

	template <typename T> 
	inline void Matrix<T>::setRows(const std::set<unsigned int>& indexes, const Matrix<T>& m)
	{
		unsigned int i = 0;

		if (indexes.size() != m.nrows() || this->m != m.ncols())
			throw std::logic_error("Error setting matrix rows: ranges are not compatible");
		for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
		{
			for (unsigned int j = 0; j < ncols(); j++)
			{
				if (*el >= n)
					throw std::logic_error("Error in setRows: trying to set a row out of matrix bounds");
				v[*el][j] = m[i][j];
			}
			i++;
		}
	}

	template <typename T> 
	inline void Matrix<T>::setColumn(unsigned int j, const Vector<T>& a)
	{	
		if (j >= m)
			throw std::logic_error("Error in setColumn: trying to set a column out of matrix bounds");
		if (this->n != a.size())
			throw std::logic_error("Error setting matrix column: ranges are not compatible");
		for (unsigned int i = 0; i < nrows(); i++)
			v[i][j] = a[i];
	}

	template <typename T> 
	inline void Matrix<T>::setColumn(unsigned int j, const Matrix<T>& a)
	{	
		if (j >= m)
			throw std::logic_error("Error in setColumn: trying to set a column out of matrix bounds");
		if (this->n != a.nrows())
			throw std::logic_error("Error setting matrix column: ranges are not compatible");
		if (a.ncols() != 1)
			throw std::logic_error("Error setting matrix column with a non-column matrix");
		for (unsigned int i = 0; i < nrows(); i++)
			v[i][j] = a[i][0];
	}


	template <typename T> 
	inline void Matrix<T>::setColumns(const std::set<unsigned int>& indexes, const Matrix<T>& a)
	{
		unsigned int j = 0;

		if (indexes.size() != a.ncols() || this->n != a.nrows())
			throw std::logic_error("Error setting matrix columns: ranges are not compatible");
		for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
		{
			for (unsigned int i = 0; i < nrows(); i++)
			{
				if (*el >= m)
					throw std::logic_error("Error in setColumns: trying to set a column out of matrix bounds");
				v[i][*el] = a[i][j];
			}
			j++;
		}
	}

	template <typename T> 
	inline void Matrix<T>::set(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes, const Matrix<T>& a)
	{
		unsigned int i = 0, j;
		if (c_indexes.size() != a.ncols() || r_indexes.size() != a.nrows())
			throw std::logic_error("Error setting matrix elements: ranges are not compatible");

		for (std::set<unsigned int>::const_iterator r_el = r_indexes.begin(); r_el != r_indexes.end(); r_el++)
		{
			if (*r_el >= n)
				throw std::logic_error("Error in set: trying to set a row out of matrix bounds");
			j = 0;
			for (std::set<unsigned int>::const_iterator c_el = c_indexes.begin(); c_el != c_indexes.end(); c_el++)
			{
				if (*c_el >= m)
					throw std::logic_error("Error in set: trying to set a column out of matrix bounds");
				v[*r_el][*c_el] = a[i][j];
				j++;
			}
			i++;
		}
	}

	template <typename T> 
	inline void Matrix<T>::set(const T* a, unsigned int n, unsigned int m)
	{
		if (this->n != n || this->m != m)
			resize(n, m);
		unsigned int k = 0;
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] = a[k++];
	}


	template <typename T>
	Matrix<T> operator+(const Matrix<T>& rhs)
	{
		return rhs;
	}

	template <typename T>
	Matrix<T> operator+(const Matrix<T>& lhs, const Matrix<T>& rhs)
	{
		if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
			throw std::logic_error("Operator+: matrices have different sizes");
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] + rhs[i][j];

		return tmp;
	}

	template <typename T>
	Matrix<T> operator+(const Matrix<T>& lhs, const T& a)
	{
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] + a;

		return tmp;
	}

	template <typename T>
	Matrix<T> operator+(const T& a, const Matrix<T>& rhs)
	{
		Matrix<T> tmp(rhs.nrows(), rhs.ncols());
		for (unsigned int i = 0; i < rhs.nrows(); i++)
			for (unsigned int j = 0; j < rhs.ncols(); j++)
				tmp[i][j] = a + rhs[i][j];

		return tmp;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator+=(const Matrix<T>& rhs)
	{
		if (m != rhs.ncols() || n != rhs.nrows())
			throw std::logic_error("Operator+=: matrices have different sizes");
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] += rhs[i][j];

		return *this;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator+=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] += a;

		return *this;
	}

	template <typename T>
	Matrix<T> operator-(const Matrix<T>& rhs)
	{	
		return (T)(-1) * rhs;
	}

	template <typename T>
	Matrix<T> operator-(const Matrix<T>& lhs, const Matrix<T>& rhs)
	{
		if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
			throw std::logic_error("Operator-: matrices have different sizes");
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] - rhs[i][j];

		return tmp;
	}

	template <typename T>
	Matrix<T> operator-(const Matrix<T>& lhs, const T& a)
	{
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] - a;

		return tmp;
	}

	template <typename T>
	Matrix<T> operator-(const T& a, const Matrix<T>& rhs)
	{
		Matrix<T> tmp(rhs.nrows(), rhs.ncols());
		for (unsigned int i = 0; i < rhs.nrows(); i++)
			for (unsigned int j = 0; j < rhs.ncols(); j++)
				tmp[i][j] = a - rhs[i][j];

		return tmp;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator-=(const Matrix<T>& rhs)
	{
		if (m != rhs.ncols() || n != rhs.nrows())
			throw std::logic_error("Operator-=: matrices have different sizes");
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] -= rhs[i][j];

		return *this;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator-=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] -= a;

		return *this;
	}

	template <typename T>
	Matrix<T> operator*(const Matrix<T>& lhs, const Matrix<T>& rhs)
	{
		if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
			throw std::logic_error("Operator*: matrices have different sizes");
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] * rhs[i][j];

		return tmp;
	}

	template <typename T>
	Matrix<T> operator*(const Matrix<T>& lhs, const T& a)
	{
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] * a;

		return tmp;
	}

	template <typename T>
	Matrix<T> operator*(const T& a, const Matrix<T>& rhs)
	{
		Matrix<T> tmp(rhs.nrows(), rhs.ncols());
		for (unsigned int i = 0; i < rhs.nrows(); i++)
			for (unsigned int j = 0; j < rhs.ncols(); j++)
				tmp[i][j] = a * rhs[i][j];

		return tmp;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator*=(const Matrix<T>& rhs)
	{
		if (m != rhs.ncols() || n != rhs.nrows())
			throw std::logic_error("Operator*=: matrices have different sizes");
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] *= rhs[i][j];

		return *this;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator*=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] *= a;

		return *this;
	}

	template <typename T>
	Matrix<T> operator/(const Matrix<T>& lhs, const Matrix<T>& rhs)
	{
		if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
			throw std::logic_error("Operator+: matrices have different sizes");
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] / rhs[i][j];

		return tmp;
	}

	template <typename T>
	Matrix<T> operator/(const Matrix<T>& lhs, const T& a)
	{
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = lhs[i][j] / a;

		return tmp;
	}

	template <typename T>
	Matrix<T> operator/(const T& a, const Matrix<T>& rhs)
	{
		Matrix<T> tmp(rhs.nrows(), rhs.ncols());
		for (unsigned int i = 0; i < rhs.nrows(); i++)
			for (unsigned int j = 0; j < rhs.ncols(); j++)
				tmp[i][j] = a / rhs[i][j];

		return tmp;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator/=(const Matrix<T>& rhs)
	{
		if (m != rhs.ncols() || n != rhs.nrows())
			throw std::logic_error("Operator+=: matrices have different sizes");
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] /= rhs[i][j];

		return *this;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator/=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] /= a;

		return *this;
	}

	template <typename T>
	Matrix<T> operator^(const Matrix<T>& lhs, const T& a)
	{
		Matrix<T> tmp(lhs.nrows(), lhs.ncols());
		for (unsigned int i = 0; i < lhs.nrows(); i++)
			for (unsigned int j = 0; j < lhs.ncols(); j++)
				tmp[i][j] = pow(lhs[i][j], a);

		return tmp;
	}

	template <typename T>
	inline Matrix<T>& Matrix<T>::operator^=(const Matrix<T>& rhs)
	{
		if (m != rhs.ncols() || n != rhs.nrows())
			throw std::logic_error("Operator^=: matrices have different sizes");
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] = pow(v[i][j], rhs[i][j]);

		return *this;
	}


	template <typename T>
	inline Matrix<T>& Matrix<T>::operator^=(const T& a)
	{
		for (unsigned int i = 0; i < n; i++)
			for (unsigned int j = 0; j < m; j++)
				v[i][j] = pow(v[i][j], a);

		return *this;
	}

	template <typename T>
	inline Matrix<T>::operator Vector<T>()
	{
		if (n > 1 && m > 1)
			throw std::logic_error("Error matrix cast to vector: trying to cast a multi-dimensional matrix");
		if (n == 1)
			return extractRow(0);
		else
			return extractColumn(0);
	}

	template <typename T>
	inline bool operator==(const Matrix<T>& a, const Matrix<T>& b)
	{
		if (a.nrows() != b.nrows() || a.ncols() != b.ncols())
			throw std::logic_error("Matrices of different size are not confrontable");
		for (unsigned i = 0; i < a.nrows(); i++)
			for (unsigned j = 0; j < a.ncols(); j++)
				if (a[i][j] != b[i][j])
					return false;
		return true;
	}

	template <typename T>
	inline bool operator!=(const Matrix<T>& a, const Matrix<T>& b)
	{
		if (a.nrows() != b.nrows() || a.ncols() != b.ncols())
			throw std::logic_error("Matrices of different size are not confrontable");
		for (unsigned i = 0; i < a.nrows(); i++)
			for (unsigned j = 0; j < a.ncols(); j++)
				if (a[i][j] != b[i][j])
					return true;
		return false;
	}



	/**
	Input/Output 
	*/
	template <typename T>
	std::ostream& operator<<(std::ostream& os, const Matrix<T>& m)
	{
		os << std::endl << m.nrows() << " " << m.ncols() << std::endl;
		for (unsigned int i = 0; i < m.nrows(); i++)
		{
			for (unsigned int j = 0; j < m.ncols() - 1; j++)
				os << std::setw(20) << std::setprecision(16) << m[i][j] << ", ";
			os << std::setw(20) << std::setprecision(16) << m[i][m.ncols() - 1] << std::endl;
		}

		return os;
	}

	template <typename T>
	std::istream& operator>>(std::istream& is, Matrix<T>& m)
	{
		int rows, cols;
		char comma;
		is >> rows >> cols;
		m.resize(rows, cols);
		for (unsigned int i = 0; i < rows; i++)
			for (unsigned int j = 0; j < cols; j++)
				is >> m[i][j] >> comma;

		return is;
	}

	template <typename T>
	T sign(const T& v)
	{
		if (v >= (T)0.0)
			return (T)1.0;
		else
			return (T)-1.0;
	}

	template <typename T>
	T dist(const T& a, const T& b)
	{
		T abs_a = (T)fabs(a), abs_b = (T)fabs(b);
		if (abs_a > abs_b)
			return abs_a * sqrt((T)1.0 + (abs_b / abs_a) * (abs_b / abs_a));
		else
			return (abs_b == (T)0.0 ? (T)0.0 : abs_b * sqrt((T)1.0 + (abs_a / abs_b) * (abs_a / abs_b)));
	}

	template <typename T>
	void svd(const Matrix<T>& A, Matrix<T>& U, Vector<T>& W, Matrix<T>& V)
	{
		int m = A.nrows(), n = A.ncols(), i, j, k, l, jj, nm;
		const unsigned int max_its = 30;
		bool flag;
		Vector<T> rv1(n);
		U = A;
		W.resize(n);
		V.resize(n, n);
		T anorm, c, f, g, h, s, scale, x, y, z;
		g = scale = anorm = (T)0.0;

		// Householder reduction to bidiagonal form
		for (i = 0; i < n; i++)
		{
			l = i + 1;
			rv1[i] = scale * g;
			g = s = scale = (T)0.0;
			if (i < m)
			{
				for (k = i; k < m; k++)
					scale += fabs(U[k][i]);
				if (scale != (T)0.0)
				{
					for (k = i; k < m; k++)
					{
						U[k][i] /= scale;
						s += U[k][i] * U[k][i];
					}
					f = U[i][i];
					g = -sign(f) * sqrt(s);
					h = f * g - s;
					U[i][i] = f - g;
					for (j = l; j < n; j++)
					{
						s = (T)0.0;
						for (k = i; k < m; k++)
							s += U[k][i] * U[k][j];
						f = s / h;
						for (k = i; k < m; k++)
							U[k][j] += f * U[k][i];
					}
					for (k = i; k < m; k++)
						U[k][i] *= scale;
				}
			}
			W[i] = scale * g;
			g = s = scale = (T)0.0;
			if (i < m && i != n - 1)
			{
				for (k = l; k < n; k++)
					scale += fabs(U[i][k]);
				if (scale != (T)0.0)
				{
					for (k = l; k < n; k++)
					{
						U[i][k] /= scale;
						s += U[i][k] * U[i][k];					
					}
					f = U[i][l];
					g = -sign(f) * sqrt(s);
					h = f * g - s;
					U[i][l] = f - g;
					for (k = l; k <n; k++)
						rv1[k] = U[i][k] / h;
					for (j = l; j < m; j++)
					{
						s = (T)0.0;
						for (k = l; k < n; k++)
							s += U[j][k] * U[i][k];
						for (k = l; k < n; k++)
							U[j][k] += s * rv1[k];
					}
					for (k = l; k < n; k++)
						U[i][k] *= scale;
				}
			}
			anorm = std::max(anorm, fabs(W[i]) + fabs(rv1[i]));
		}
		// Accumulation of right-hand transformations
		for (i = n - 1; i >= 0; i--)
		{
			if (i < n - 1) 
			{
				if (g != (T)0.0)
				{
					for (j = l; j < n; j++)
						V[j][i] = (U[i][j] / U[i][l]) / g;
					for (j = l; j < n; j++)
					{
						s = (T)0.0;
						for (k = l; k < n; k++)
							s += U[i][k] * V[k][j];
						for (k = l; k < n; k++)
							V[k][j] += s * V[k][i];
					}
				}
				for (j = l; j < n; j++)
					V[i][j] = V[j][i] = (T)0.0;
			}
			V[i][i] = (T)1.0;
			g = rv1[i];
			l = i;
		}
		// Accumulation of left-hand transformations
		for (i = std::min(m, n) - 1; i >= 0; i--)
		{
			l = i + 1;
			g = W[i];
			for (j = l; j < n; j++)
				U[i][j] = (T)0.0;
			if (g != (T)0.0)
			{
				g = (T)1.0 / g;
				for (j = l; j < n; j++)
				{
					s = (T)0.0;
					for (k = l; k < m; k++)
						s += U[k][i] * U[k][j];
					f = (s / U[i][i]) * g;
					for (k = i; k < m; k++)
						U[k][j] += f * U[k][i];
				}
				for (j = i; j < m; j++)
					U[j][i] *= g;
			}
			else
				for (j = i; j < m; j++)
					U[j][i] = (T)0.0;
			U[i][i]++;
		}
		// Diagonalization of the bidiagonal form: loop over singular values, and over allowed iterations.
		for (k = n - 1; k >= 0; k--)
		{
			for (unsigned int its = 0; its < max_its; its++)
			{
				flag = true;
				for (l = k; l >= 0; l--) // FIXME: in NR it was l >= 1 but there subscripts start from one
				{ // Test for splitting
					nm = l - 1; // Note that rV[0] is always zero
					if ((T)(fabs(rv1[l]) + anorm) == anorm)
					{
						flag = false;
						break;
					}
					if ((T)(fabs(W[nm]) + anorm) == anorm)
						break;
				}
				if (flag)
				{
					// Cancellation of rv1[l], if l > 0 FIXME: it was l > 1 in NR
					c = (T)0.0;
					s = (T)1.0;
					for (i = l; i <= k; i++)
					{
						f = s * rv1[i];
						rv1[i] *= c;
						if ((T)(fabs(f) + anorm) == anorm)
							break;
						g = W[i];
						h = dist(f, g);
						W[i] = h;
						h = (T)1.0 / h;
						c = g * h;
						s = -f * h;
						for (j = 0; j < m; j++)
						{
							y = U[j][nm];
							z = U[j][i];
							U[j][nm] = y * c + z * s;
							U[j][i] = z * c - y * s;
						}
					}
				}
				z = W[k];
				if (l == k)
				{  // Convergence
					if (z < (T)0.0)
					{ // Singular value is made nonnegative
						W[k] = -z;
						for (j = 0; j < n; j++)
							V[j][k] = -V[j][k];
					}
					break;
				}
				if (its == max_its)
					throw std::logic_error("Error svd: no convergence in the maximum number of iterations");
				x = W[l];
				nm = k - 1;
				y = W[nm];
				g = rv1[nm];
				h = rv1[k];
				f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
				g = dist(f, (T)1.0);
				f = ((x - z) * (x + z) + h * ((y / (f + sign(f)*fabs(g))) - h)) / x;
				c = s = (T)1.0; // Next QR transformation
				for (j = l; j <= nm; j++)
				{
					i = j + 1;
					g = rv1[i];
					y = W[i];
					h = s * g;
					g *= c;
					z = dist(f, h);
					rv1[j] = z;
					c = f / z;
					s = h / z;
					f = x * c + g * s;
					g = g * c - x * s;
					h = y * s;
					y *= c;
					for (jj = 0; jj < n; jj++)
					{
						x = V[jj][j];
						z = V[jj][i];
						V[jj][j] = x * c + z * s;
						V[jj][i] = z * c - x * s;
					}
					z = dist(f, h);
					W[j] = z; 
					if (z != 0) // Rotation can be arbitrary if z = 0
					{
						z = (T)1.0 / z;
						c = f * z;
						s = h * z;
					}
					f = c * g + s * y;
					x = c * y - s * g;
					for (jj = 0; jj < m; jj++)
					{
						y = U[jj][j];
						z = U[jj][i];
						U[jj][j] = y * c + z * s;
						U[jj][i] = z * c - y * s;
					}
				}
				rv1[l] = (T)0.0;
				rv1[k] = f;
				W[k] = x;
			}
		}	
	}

	template <typename T>
	Matrix<T> pinv(const Matrix<T>& A)
	{
		Matrix<T> U, V, x, tmp(A.ncols(), A.nrows());
		Vector<T> W;
		CanonicalBaseVector<T> e(0, A.nrows());
		svd(A, U, W, V);
		for (unsigned int i = 0; i < A.nrows(); i++)
		{
			e.reset(i);
			tmp.setColumn(i, dot_prod(dot_prod(dot_prod(V, Matrix<double>(DIAG, 1.0 / W, 0.0, W.size(), W.size())), t(U)), e));
		}

		return tmp;
	}

	template <typename T>
	int lu(const Matrix<T>& A, Matrix<T>& LU, Vector<unsigned int>& index)
	{
		if (A.ncols() != A.nrows())
			throw std::logic_error("Error in LU decomposition: matrix must be squared");
		int i, p, j, k, n = A.ncols(), ex;
		T val, tmp;
		Vector<T> d(n);
		LU = A;
		index.resize(n);

		ex = 1;
		for (i = 0; i < n; i++)
		{
			index[i] = i;
			val = (T)0.0;
			for (j = 0; j < n; j++)
				val = std::max(val, (T)fabs(LU[i][j]));
			if (val == (T)0.0)
				std::logic_error("Error in LU decomposition: matrix was singular");
			d[i] = val;
		}

		for (k = 0; k < n - 1; k++)
		{
			p = k;
			val = fabs(LU[k][k]) / d[k];
			for (i = k + 1; i < n; i++)
			{
				tmp = fabs(LU[i][k]) / d[i];
				if (tmp > val)
				{
					val = tmp;
					p = i;
				}
			}
			if (val == (T)0.0)
				std::logic_error("Error in LU decomposition: matrix was singular");
			if (p > k)
			{
				ex = -ex;
				std::swap(index[k], index[p]);
				std::swap(d[k], d[p]);
				for (j = 0; j < n; j++)
					std::swap(LU[k][j], LU[p][j]);
			}

			for (i = k + 1; i < n; i++)
			{
				LU[i][k] /= LU[k][k];
				for (j = k + 1; j < n; j++)
					LU[i][j] -= LU[i][k] * LU[k][j];
			}
		}
		if (LU[n - 1][n - 1] == (T)0.0)
			std::logic_error("Error in LU decomposition: matrix was singular");

		return ex;
	}

	template <typename T>
	Vector<T> lu_solve(const Matrix<T>& LU, const Vector<T>& b, Vector<unsigned int>& index)
	{
		if (LU.ncols() != LU.nrows())
			throw std::logic_error("Error in LU solve: LU matrix should be squared");
		unsigned int n = LU.ncols();
		if (b.size() != n)
			throw std::logic_error("Error in LU solve: b vector must be of the same dimensions of LU matrix");
		Vector<T> x((T)0.0, n);
		int i, j, p;
		T sum;

		p = index[0];
		x[0] = b[p];

		for (i = 1; i < n; i++)
		{
			sum = (T)0.0;
			for (j = 0; j < i; j++)
				sum += LU[i][j] * x[j];
			p = index[i];
			x[i] = b[p] - sum;
		}
		x[n - 1] /= LU[n - 1][n - 1];
		for (i = n - 2; i >= 0; i--)
		{
			sum = (T)0.0;
			for (j = i + 1; j < n; j++)
				sum += LU[i][j] * x[j];
			x[i] = (x[i] - sum) / LU[i][i];
		}
		return x;
	}

	template <typename T>
	void lu_solve(const Matrix<T>& LU, Vector<T>& x, const Vector<T>& b, Vector<unsigned int>& index)
	{
		x = lu_solve(LU, b, index);
	}

	template <typename T>
	Matrix<T> lu_inverse(const Matrix<T>& A)
	{
		if (A.ncols() != A.nrows())
			throw std::logic_error("Error in LU invert: matrix must be squared");	
		unsigned int n = A.ncols();
		Matrix<T> A1(n, n), LU;
		Vector<unsigned int> index;

		lu(A, LU, index);
		CanonicalBaseVector<T> e(0, n);
		for (unsigned i = 0; i < n; i++)
		{
			e.reset(i);
			A1.setColumn(i, lu_solve(LU, e, index));
		}

		return A1;
	}

	template <typename T>
	T lu_det(const Matrix<T>& A)
	{
		if (A.ncols() != A.nrows())
			throw std::logic_error("Error in LU determinant: matrix must be squared");	
		unsigned int d;
		Matrix<T> LU;
		Vector<unsigned int> index;

		d = lu(A, LU, index);

		return d * prod(LU.extractDiag());
	}

	template <typename T>
	void cholesky(const Matrix<T> A, Matrix<T>& LL) 
	{
		if (A.ncols() != A.nrows())
			throw std::logic_error("Error in Cholesky decomposition: matrix must be squared");
		register int i, j, k, n = A.ncols();
		register double sum;
		LL = A;

		for (i = 0; i < n; i++)
		{
			for (j = i; j < n; j++)
			{
				sum = LL[i][j];
				for (k = i - 1; k >= 0; k--)
					sum -= LL[i][k] * LL[j][k];
				if (i == j) 
				{
					if (sum <= 0.0)
						throw std::logic_error("Error in Cholesky decomposition: matrix is not postive definite");
					LL[i][i] = sqrt(sum);
				}
				else
					LL[j][i] = sum / LL[i][i];
			}
			for (k = i + 1; k < n; k++)
				LL[i][k] = LL[k][i];
		} 
	}

	template <typename T>
	Matrix<T> cholesky(const Matrix<T> A) 
	{
		Matrix<T> LL;
		cholesky(A, LL);

		return LL;
	}

	template <typename T>
	Vector<T> cholesky_solve(const Matrix<T>& LL, const Vector<T>& b)
	{
		if (LL.ncols() != LL.nrows())
			throw std::logic_error("Error in Cholesky solve: matrix must be squared");
		unsigned int n = LL.ncols();
		if (b.size() != n)
			throw std::logic_error("Error in Cholesky decomposition: b vector must be of the same dimensions of LU matrix");
		Vector<T> x, y;

		/* Solve L * y = b */
		forward_elimination(LL, y, b);
		/* Solve L^T * x = y */
		backward_elimination(LL, x, y);

		return x;
	}

	template <typename T>
	void cholesky_solve(const Matrix<T>& LL, Vector<T>& x, const Vector<T>& b)
	{
		x = cholesky_solve(LL, b);
	}

	template <typename T>
	void forward_elimination(const Matrix<T>& L, Vector<T>& y, const Vector<T> b)
	{
		if (L.ncols() != L.nrows())
			throw std::logic_error("Error in Forward elimination: matrix must be squared (lower triangular)");
		if (b.size() != L.nrows())
			throw std::logic_error("Error in Forward elimination: b vector must be of the same dimensions of L matrix");
		register int i, j, n = b.size();
		y.resize(n);

		y[0] = b[0] / L[0][0];
		for (i = 1; i < n; i++)
		{
			y[i] = b[i];
			for (j = 0; j < i; j++)
				y[i] -= L[i][j] * y[j];
			y[i] = y[i] / L[i][i];
		}
	}

	template <typename T>
	Vector<T> forward_elimination(const Matrix<T>& L, const Vector<T> b)
	{
		Vector<T> y;
		forward_elimination(L, y, b);

		return y;
	}

	template <typename T>
	void backward_elimination(const Matrix<T>& U, Vector<T>& x, const Vector<T>& y)
	{
		if (U.ncols() != U.nrows())
			throw std::logic_error("Error in Backward elimination: matrix must be squared (upper triangular)");
		if (y.size() != U.nrows())
			throw std::logic_error("Error in Backward elimination: b vector must be of the same dimensions of U matrix");
		register int i, j, n = y.size();
		x.resize(n);

		x[n - 1] = y[n - 1] / U[n - 1][n - 1];
		for (i = n - 2; i >= 0; i--)
		{
			x[i] = y[i];
			for (j = i + 1; j < n; j++)
				x[i] -= U[i][j] * x[j];
			x[i] = x[i] / U[i][i];
		}
	}

	template <typename T>
	Vector<T> backward_elimination(const Matrix<T>& U, const Vector<T> y)
	{
		Vector<T> x;
		forward_elimination(U, x, y);

		return x;
	}

	/* Setting default linear systems machinery */

#define det lu_det
#define inverse lu_inverse
#define solve lu_solve

	/* Random */

	template <typename T>
	void random(Matrix<T>& m)
	{
		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				m[i][j] = (T)(rand() / double(RAND_MAX));
	}

	/**
	Aggregate functions
	*/

	template <typename T>
	Vector<T> sum(const Matrix<T>& m)
	{
		Vector<T> tmp((T)0, m.ncols());
		for (unsigned int j = 0; j < m.ncols(); j++)
			for (unsigned int i = 0; i < m.nrows(); i++)
				tmp[j] += m[i][j];
		return tmp;
	}

	template <typename T>
	Vector<T> r_sum(const Matrix<T>& m)
	{
		Vector<T> tmp((T)0, m.nrows());
		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				tmp[i] += m[i][j];
		return tmp;
	}

	template <typename T>
	T all_sum(const Matrix<T>& m)
	{
		T tmp = (T)0;
		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				tmp += m[i][j];
		return tmp;
	}

	template <typename T>
	Vector<T> prod(const Matrix<T>& m)
	{
		Vector<T> tmp((T)1, m.ncols());
		for (unsigned int j = 0; j < m.ncols(); j++)
			for (unsigned int i = 0; i < m.nrows(); i++)
				tmp[j] *= m[i][j];
		return tmp;
	}

	template <typename T>
	Vector<T> r_prod(const Matrix<T>& m)
	{
		Vector<T> tmp((T)1, m.nrows());
		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				tmp[i] *= m[i][j];
		return tmp;
	}

	template <typename T>
	T all_prod(const Matrix<T>& m)
	{
		T tmp = (T)1;
		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				tmp *= m[i][j];
		return tmp;
	}

	template <typename T>
	Vector<T> mean(const Matrix<T>& m)
	{
		Vector<T> res((T)0, m.ncols());
		for (unsigned int j = 0; j < m.ncols(); j++)
		{
			for (unsigned int i = 0; i < m.nrows(); i++)
				res[j] += m[i][j];
			res[j] /= m.nrows();
		}

		return res;
	}

	template <typename T>
	Vector<T> r_mean(const Matrix<T>& m)
	{
		Vector<T> res((T)0, m.rows());
		for (unsigned int i = 0; i < m.nrows(); i++)
		{
			for (unsigned int j = 0; j < m.ncols(); j++)
				res[i] += m[i][j];
			res[i] /= m.nrows();
		}

		return res;
	}

	template <typename T>
	T all_mean(const Matrix<T>& m)
	{
		T tmp = (T)0;
		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				tmp += m[i][j];
		return tmp / (m.nrows() * m.ncols());
	}

	template <typename T>
	Vector<T> var(const Matrix<T>& m, bool sample_correction = false)
	{
		Vector<T> res((T)0, m.ncols());
		unsigned int n = m.nrows();
		double sum, ssum;
		for (unsigned int j = 0; j < m.ncols(); j++)
		{	
			sum = (T)0.0; ssum = (T)0.0;
			for (unsigned int i = 0; i < m.nrows(); i++)
			{
				sum += m[i][j];
				ssum += (m[i][j] * m[i][j]);
			}
			if (!sample_correction)
				res[j] = (ssum / n) - (sum / n) * (sum / n);
			else
				res[j] = n * ((ssum / n) - (sum / n) * (sum / n)) / (n - 1);		 
		}

		return res;
	}

	template <typename T>
	Vector<T> stdev(const Matrix<T>& m, bool sample_correction = false)
	{
		return sqrt(var(m, sample_correction));
	}

	template <typename T>
	Vector<T> r_var(const Matrix<T>& m, bool sample_correction = false)
	{
		Vector<T> res((T)0, m.nrows());
		double sum, ssum;
		unsigned int n = m.ncols();
		for (unsigned int i = 0; i < m.nrows(); i++)
		{	
			sum = 0.0; ssum = 0.0;
			for (unsigned int j = 0; j < m.ncols(); j++)
			{
				sum += m[i][j];
				ssum += (m[i][j] * m[i][j]);
			}
			if (!sample_correction)
				res[i] = (ssum / n) - (sum / n) * (sum / n);
			else
				res[i] = n * ((ssum / n) - (sum / n) * (sum / n)) / (n - 1);
		}

		return res;
	}

	template <typename T>
	Vector<T> r_stdev(const Matrix<T>& m, bool sample_correction = false)
	{
		return sqrt(r_var(m, sample_correction));
	}

/*	template <typename T>
	Vector<T> max(const Matrix<T>& m)
	{
		Vector<T> res(m.ncols());
		double value;
		for (unsigned int j = 0; j < m.ncols(); j++)
		{
			value = m[0][j];
			for (unsigned int i = 1; i < m.nrows(); i++)
				value = std::max(m[i][j], value);
			res[j] = value;
		}

		return res;
	}

	template <typename T>
	Vector<T> r_max(const Matrix<T>& m)
	{
		Vector<T> res(m.nrows());
		double value;
		for (unsigned int i = 0; i < m.nrows(); i++)
		{
			value = m[i][0];
			for (unsigned int j = 1; j < m.ncols(); j++)
				value = std::max(m[i][j], value);
			res[i] = value;
		}

		return res;
	}

	template <typename T>
	Vector<T> min(const Matrix<T>& m)
	{
		Vector<T> res(m.ncols());
		double value;
		for (unsigned int j = 0; j < m.ncols(); j++)
		{
			value = m[0][j];
			for (unsigned int i = 1; i < m.nrows(); i++)
				value = std::min(m[i][j], value);
			res[j] = value;
		}

		return res;
	}

	template <typename T>
	Vector<T> r_min(const Matrix<T>& m)
	{
		Vector<T> res(m.nrows());
		double value;
		for (unsigned int i = 0; i < m.nrows(); i++)
		{
			value = m[i][0];
			for (unsigned int j = 1; j < m.ncols(); j++)
				value = std::min(m[i][j], value);
			res[i] = value;
		}

		return res;
	}



	/**
	Single element mathematical functions
	*/

	template <typename T>
	Matrix<T> exp(const Matrix<T>&m)
	{
		Matrix<T> tmp(m.nrows(), m.ncols());

		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				tmp[i][j] = exp(m[i][j]);

		return tmp;
	}

	template <typename T>
	Matrix<T> sqrt(const Matrix<T>&m)
	{
		Matrix<T> tmp(m.nrows(), m.ncols());

		for (unsigned int i = 0; i < m.nrows(); i++)
			for (unsigned int j = 0; j < m.ncols(); j++)
				tmp[i][j] = sqrt(m[i][j]);

		return tmp;
	}

	/**
	Matrix operators
	*/

	template <typename T>
	Matrix<T> kron(const Vector<T>& b, const Vector<T>& a)
	{
		Matrix<T> tmp(b.size(), a.size());
		for (unsigned int i = 0; i < b.size(); i++)
			for (unsigned int j = 0; j < a.size(); j++)
				tmp[i][j] = a[j] * b[i];

		return tmp;
	}

	template <typename T>
	Matrix<T> t(const Matrix<T>& a)
	{
		Matrix<T> tmp(a.ncols(), a.nrows());
		for (unsigned int i = 0; i < a.nrows(); i++)
			for (unsigned int j = 0; j < a.ncols(); j++)
				tmp[j][i] = a[i][j];

		return tmp;
	}

	template <typename T>
	Matrix<T> dot_prod(const Matrix<T>& a, const Matrix<T>& b)
	{
		if (a.ncols() != b.nrows())
			throw std::logic_error("Error matrix dot product: dimensions of the matrices are not compatible");
		Matrix<T> tmp(a.nrows(), b.ncols());
		for (unsigned int i = 0; i < tmp.nrows(); i++)
			for (unsigned int j = 0; j < tmp.ncols(); j++)
			{
				tmp[i][j] = (T)0;
				for (unsigned int k = 0; k < a.ncols(); k++)
					tmp[i][j] += a[i][k] * b[k][j];
			}

			return tmp;
	}

	template <typename T>
	Matrix<T> dot_prod(const Matrix<T>& a, const Vector<T>& b)
	{
		if (a.ncols() != b.size())
			throw std::logic_error("Error matrix dot product: dimensions of the matrix and the vector are not compatible");
		Matrix<T> tmp(a.nrows(), 1);
		for (unsigned int i = 0; i < tmp.nrows(); i++)
		{
			tmp[i][0] = (T)0;
			for (unsigned int k = 0; k < a.ncols(); k++)
				tmp[i][0] += a[i][k] * b[k];
		}

		return tmp;
	}

	template <typename T>
	Matrix<T> dot_prod(const Vector<T>& a, const Matrix<T>& b)
	{
		if (a.size() != b.ncols())
			throw std::logic_error("Error matrix dot product: dimensions of the vector and matrix are not compatible");
		Matrix<T> tmp(1, b.ncols());
		for (unsigned int j = 0; j < tmp.ncols(); j++)
		{
			tmp[0][j] = (T)0;
			for (unsigned int k = 0; k < a.size(); k++)
				tmp[0][j] += a[k] * b[k][j];
		}

		return tmp;
	}

	template <typename T>
	inline Matrix<double> rank(const Matrix<T> m)
	{
		Matrix<double> tmp(m.nrows(), m.ncols());
		for (unsigned int j = 0; j < m.ncols(); j++)
			tmp.setColumn(j, rank<T>(m.extractColumn(j)));

		return tmp;                  
	}

	template <typename T>
	inline Matrix<double> r_rank(const Matrix<T> m)
	{
		Matrix<double> tmp(m.nrows(), m.ncols());
		for (unsigned int i = 0; i < m.nrows(); i++)
			tmp.setRow(i, rank<T>(m.extractRow(i)));

		return tmp;                  
	}
}


#endif // define _ARRAY_HH_
